President Serzh Sarkisian held through his aides on Monday fresh talks with major Armenian political parties on a package of controversial constitutional amendments which he plans to put on a referendum later this year.

Two members of a presidential commission that has drafted those amendments met separately with the parliamentary leaders of the opposition Zharangutyun and Dashnaktsutyun party. They are scheduled to meet with other parliamentary factions on Tuesday.

The talks follow a series of consultations which Sarkisian personally held last week with the leaders of a dozen parties that now seem ready, in principle, to back his constitutional package envisaging Armenia’s transformation into a parliamentary republic. Still, some of those parties, which claim to be in opposition to the government, object to several amendments to the Armenian constitution proposed by the commission.

The most controversial of those provisions stipulates that Armenian parliamentary elections must necessarily produce a clear winner that will get the majority of seats in the National Assembly. That would require a second round of voting between the two top election contenders. Critics say this clause is designed to spare the ruling Republican Party of Armenia (HHK) the need to cut genuine power-sharing deals with other factions.

The HHK’s parliamentary leader, Vahram Baghdasarian, said over the weekend that the Sarkisian administration has altered the controversial clause. In his words, a parliamentary run-off vote would not have to be held if election winners manage to form a coalition government after the first round.

Zharangutyun’s Ruben Hakobian confirmed this after the meeting with the two presidential aides. “But even that [change] is not enough to address our concerns,” he told RFE/RL’s Armenian service (Azatutyun.am).

Zharangutyun and another opposition party, the Armenian National Congress (HAK), reject the constitutional reform as a whole, saying that it would only help Sarkisian indefinitely extend his rule. Accordingly, the leaders of the two parties refused to meet with the president last week.

The draft amendments have undergone changes despite being formally sent to the National Assembly by Sarkisian earlier this month. The parliament dominated by government loyalists will start debating them in September.